phantomjs testing script to evaluate a page, wait for a response from MathJax, and close the page. Use in conjunction with mathjax_test.js script; all this does is load the page so any errors flagged from the mathjax_test code is posted to the error database. the two scripts need each other in order to test the file.
This script expects a single url to open, evaluate, and close. If there are TeX or MathJax errors, they will be flagged and posted through the javascript contained in the url page.
The way I use this is to loop through a tree of html files after a build, invoking this script on each file in the tree. When that process ends, the error database contains all the flagged errors found in the tree.

MathJax testing for TeX and rendering errors. Create HTML page (with math) to include the MathJax library and then include this file. When the page is loaded, the js console will show when errors are encountered and the data about the error will be POSTed via ajax to a rest-type service named here as 'service/mathmltest'. That service should accept the JSON string, convert to data and save it (I save mine in a MongoDB document).
You can also have a phantomjs instance loop over all the html files in a directory to load each file and accumulate error reports from the ajax-posted data. That assumes you have access to how the html is created so you can insert the call to include the js file of course.